A Local Search 4/3-approximation Algorithm for the Minimum 3-path Partition Problem
Given a graph \(G = (V, E)\), the 3-path partition problem is to find a minimum collection of vertex-disjoint paths each of order at most 3 to cover all the vertices of V. It is different from but closely related to the well-known 3-set cover problem. The best known approximation algorithm for the 3-path partition problem was proposed recently and has a ratio 13/9. Here we present a local search algorithm and show, by an amortized analysis, that it is a 4/3-approximation. This ratio matches up to the best approximation ratio for the 3-set cover problem.
Keywordsk-path partition Path cover k-set cover Approximation algorithms Local search Amortized analysis
YC and AZ were supported by the NSFC Grants 11771114 and 11571252; YC was also supported by the China Scholarship Council Grant 201508330054. RG, GL and YX were supported by the NSERC Canada. LL was supported by the China Scholarship Council Grant No. 201706315073, and the Fundamental Research Funds for the Central Universities Grant No. 20720160035. WT was supported in part by funds from the College of Engineering and Computing at the Georgia Southern University.
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